Conditional Independence by Typing

A central goal of probabilistic programming languages (PPLs) is to separate modelling from inference. However, this goal is hard to achieve in practice. Users are often forced to re-write their models to improve efficiency of inference or meet restrictions imposed by the PPL. Conditional independence (CI) relationships among parameters are a crucial aspect of probabilistic models that capture a qualitative summary of the specified model and can facilitate more efficient inference. We present an information flow type system for probabilistic programming that captures conditional independence (CI) relationships and show that, for a well-typed program in our system, the distribution it implements is guaranteed to have certain CI-relationships. Further, by using type inference, we can statically deduce which CI-properties are present in a specified model. As a practical application, we consider the problem of how to perform inference on models with mixed discrete and continuous parameters. Inference on such models is challenging in many existing PPLs, but can be improved through a workaround, where the discrete parameters are used implicitly , at the expense of manual model re-writing. We present a source-to-source semantics-preserving transformation, which uses our CI-type system to automate this workaround by eliminating the discrete parameters from a probabilistic program. The resulting program can be seen as a hybrid inference algorithm on the original program, where continuous parameters can be drawn using efficient gradient-based inference methods, while the discrete parameters are inferred using variable elimination. We implement our CI-type system and its example application in SlicStan: a compositional variant of Stan. 1

Forgetting in Answer Set Programming – A Survey

Forgetting – or variable elimination – is an operation that allows the removal, from a knowledge base, of middle variables no longer deemed relevant. In recent years, many different approaches for forgetting in Answer Set Programming have been proposed, in the form of specific operators, or classes of such operators, commonly following different principles and obeying different properties. Each such approach was developed to address some particular view on forgetting, aimed at obeying a specific set of properties deemed desirable in such view, but a comprehensive and uniform overview of all the existing operators and properties is missing. In this article, we thoroughly examine existing properties and (classes of) operators for forgetting in Answer Set Programming, drawing a complete picture of the landscape of these classes of forgetting operators, which includes many novel results on relations between properties and operators, including considerations on concrete operators to compute results of forgetting and computational complexity. Our goal is to provide guidance to help users in choosing the operator most adequate for their application requirements.

Determining residuary resistance per unit weight of displacement with Symbolic Regression and Gradient Boosted Tree algorithms

Determining the residuary resistance per unit weight of displacement is one of the key factors in the design of vessels. In this paper, the authors utilize two novel methods – Symbolic Regression (SR) and Gradient Boosted Trees (GBT) to achieve a model which can be used to calculate the value of residuary resistance per unit weight, of displacement from the longitudinal position of the center of buoyancy, prismatic coefficient, length-displacement ratio, beam-draught ratio, length-beam ratio, and Froude number. This data is given as results of 308 experiments provided as a part of a publicly available dataset. The results are evaluated using the coefficient of determination (R2) and Mean Absolute Percentage Error (MAPE). Pre-processing, in the shape of correlation analysis combined with variable elimination and variable scaling, is applied to the dataset. The results show that while both methods achieve regression results, the result of regression of SR is relatively poor in comparison to GBT. Both methods provide slightly poorer, but comparable results to previous research focussing on the use of “black-box” methods, such as neural networks. The elimination of variables does not show a high influence on the modeling performance in the presented case, while variable scaling does achieve better results compared to the models trained with the non-scaled dataset.

Algebraic Solution of Tropical Polynomial Optimization Problems

We consider constrained optimization problems defined in the tropical algebra setting on a linearly ordered, algebraically complete (radicable) idempotent semifield (a semiring with idempotent addition and invertible multiplication). The problems are to minimize the objective functions given by tropical analogues of multivariate Puiseux polynomials, subject to box constraints on the variables. A technique for variable elimination is presented that converts the original optimization problem to a new one in which one variable is removed and the box constraint for this variable is modified. The novel approach may be thought of as an extension of the Fourier–Motzkin elimination method for systems of linear inequalities in ordered fields to the issue of polynomial optimization in ordered tropical semifields. We use this technique to develop a procedure to solve the problem in a finite number of iterations. The procedure includes two phases: backward elimination and forward substitution of variables. We describe the main steps of the procedure, discuss its computational complexity and present numerical examples.

Research on Enhanced Detection of Benzoic Acid Additives in Liquid Food Based on Terahertz Metamaterial Devices

It is very important for human health to supervise the use of food additives, because excessive use of food additives will cause harm to the human body, especially lead to organ failures and even cancers. Therefore, it is important to realize high-sensibility detection of benzoic acid, a widely used food additive. Based on the theory of electromagnetism, this research attempts to design a terahertz-enhanced metamaterial resonator, using a metamaterial resonator to achieve enhanced detection of benzoic acid additives by using terahertz technology. The absorption peak of the metamaterial resonator is designed to be 1.95 THz, and the effectiveness of the metamaterial resonator is verified. Firstly, the original THz spectra of benzoic acid aqueous solution samples based on metamaterial are collected. Secondly, smoothing, multivariate scattering correction (MSC), and smoothing combined with first derivative (SG + 1 D) methods are used to preprocess the spectra to study the better spectral pretreatment methods. Then, Uninformative Variable Elimination (UVE) and Competitive Adaptive Reweighted Sampling (CARS) are used to explore the optimal terahertz band selection method. Finally, Partial Least Squares (PLS) and Least square support vector machine (LS-SVM) models are established, respectively, to realize the enhanced detection of benzoic acid additives. The LS-SVM model combined with CARS has the best effect, with the correlation coefficient of prediction set (Rp) is 0.9953, the root mean square error of prediction set (RMSEP) is 7.3 × 10−6, and the limit of detection (LOD) is 2.3610 × 10−5 g/mL. The research results lay a foundation for THz spectral analysis of benzoic acid additives, so that THz technology-based detection of benzoic acid additives in food can reach requirements stipulated in the national standard. This research is of great significance for promoting the detection and analysis of trace additives in food, whose results can also serve as a reference to the detection of antibiotic residues, banned additives, and other trace substances.

Chapter 30. Reasoning with Quantified Boolean Formulas

The implementation of effective reasoning tools for deciding the satisfiability of Quantified Boolean Formulas(QBFs) is an important research issue in Artificial Intelligence and Computer Science. Indeed, QBF solvers have already been proposed for many reasoning tasks in knowledge representation and reasoning, in automated planning and in formal methods for computer aided design. Even more, since QBF reasoning is the prototypical PSPACE problem, the reduction of many other decision problems in PSPACE are readily available. For these reasons, in the last few years several decision procedures for QBFs have been proposed and implemented, mostly based either on search or on variable elimination, or on a combination of the two. In this chapter, after a brief recap of the basic terminology and notation about QBFs, we briefly review various applications of QBF reasoning that have been recently proposed, and then we focus on the description of the main approaches which are at the basis of currently available solvers for prenex QBFs in conjunctive normal form (CNF). Other approaches and extensions to non prenex, non CNF QBFs are briefly reviewed at the end of the chapter.

PROBABILISTIC INFERENCE IN BAYESIAN INSURANCE NETWORK

In this paper, the technique to solve the prediction problem of reparation of the financial losses caused by a road traffic accident is solved. Exact inference is represented using the Sum-Product Variable Elimination algorithm, Sum-Product Variable Elimination algorithm for computing conditional probabilities, Max-Product Variable Elimination algorithm for MAP, Max-Sum-Product Variable Elimination algorithm for marginal MAP. Reasoning patterns are presented graphically and descriptively.